Cylindrical rod geometries are common for laser crystals, such as Nd:YAG, and have been widely utilized because the desired TEMOO laser mode exhibits radial and azimuthal symmetry. Large lamp pumped laserheads typically use water-cooled rods.
As reported by Baer et al. in his early work with diode pumped systems, a rod is a suitable geometry for an isotropic crystal and a cylindrically symmetric pumped volume. If the circumference of the rod uniformly contacts a heat sink, with low thermal impedance, then the temperature at the circumference of the rod is held to a uniform temperature close to that of the heat sink. With a cylindrical rod geometry the heat flow and resultant thermal gradients are radial. When the material exhibits a non-zero variation in the index of refraction, as a function of temperature, the radial gradients in the index of refraction as a function of radius result in a circular thermal lens. Any bulge or distortion of the pumped surface of such a rod contributes to the magnitude of the thermal lens. A composite is generated by the sum of the focussing effects of the index of refraction variation and the surface distortion. Longitudinally pumping of rods made of isotropic materials, uniformly heatsunk around the rod's circumference, or mounted in other ways that allow radial heat flow, generate index variations and surface distortions. The composite thermal lens is therefore radially symmetric; that is, the curves of constant phase are circles.
In low power laser systems, less than 2 W, the thermal lens can often be ignored. This is because the focussing power of the thermal lens in a low power system is typically much lower than the focussing power of other optics in the laserhead, such as an end mirror with a curved surface. In high power laser systems, greater than 2 W, the focussing or defocussing power of the thermal lens can be significant; the focussing power can be comparable to or even much greater than the focussing power of other optics in the laser resonator. Strong and weak thermal lens focussing powers are defined as follows:
Strong thermal lens: The focussing power of the pump induced lens is at least comparable to that of the other optics in the laser resonator. A strong thermal lens significantly changes the size and divergence of a laser resonator eigen mode within the resonator. PA1 Weak thermal lens: The focussing power of the pump induced lens is substantially lower than that of the other optics in the laser resonator such as mirrors and typical lenses. The other optics in the laser resonator dictate the size and divergence of the resonator eigen mode.
There are key differences between Nd:YVO4 and Nd:YAG, primarily Nd:YAG is nearly isotropic in its crystal properties while Nd:YVO4 is strongly anisotropic. For this reason, given a round pump source, it is relatively straightforward to generate a round thermal lens in Nd:YAG. Investigators have reported that it is difficult to produce a round thermal lens in an anisotropic material such as Nd:YLF or Nd:YVO4. Such materials, and in particular Nd:YVO4, have optical, thermal and mechanical characteristics that are greatly different along the ordinary and extraordinary crystallographic axes. Overall radial symmetry of the thermal lens is not expected.
With Nd:YVO4, the thermal expansion coefficient in a direction parallel to the "a" axis is about 2.5 times smaller than that parallel to the "c" axis. The variation of the index of refraction, as a function of temperature, is different by about a factor of 2.8 along the "c" and "a" axes. Additionally, there is more than a 10% difference between the indices of refraction for the two crystallographic axes. The material Nd:YVO4 is strongly anisotropic that a radially symmetric thermal lens is difficult to produce.
FIG. 1 illustrates the contours of constant phase for a thermal lens that was generated in Nd:YVO4 with a diode pump source. A pump power of 15 W was focussed to a 0.6 mm diameter spot. The thermal lens was measured by placing it in a typical shear interferometer using standard, commercially available fringe capture software. The peak to valley phase difference is 2.9 radians; this corresponds to a very strong focussing power (the effective focal length of the lens is approximately 10 cm). In this case, the constant phase contours are ellipses and the thermal lens is, therefore, "elliptical". This elliptical shape results in a different focal power in one plane than in the other, or fx/fy.noteq.1, where fx and fy are the focal lengths of the thermal lens in the x and y planes. In the example of FIG. 1, fx/fy=1.2. For a "circular" lens, the value of fx/fy does not equal 1. This would approximate a simple spherical lens. An elliptical thermal lens is defined as one where fx/fy does not equal 1, and a circular thermal lens is the special case of fx/fy.about.1. Either fx or fy can have negative values. This results from a value of dn/dt that is negative, as is the case with Nd:YLF.
Researchers have reported elliptical, astigmatic and other non-circular thermal lenses in anisotropic media, particularly Nd:YVO4. See for example Henry Plaessman, Sean A. Re, Joseph J. Alonis, David L. Vecht and William Grossman, Opt. Lett. 18, 1420 (1993). The problem with non-radially symmetric thermal lenses that are strong in a laser resonator is that it is difficult to generate a round, non-astigmatic laser beam with very high beam quality.
With a variety of complex configurations the ellipticity can be reduced. For example, special compensating lenses can be used. However, such methods are costly and typically cannot work for a range of pump power, since the thermal lens magnitude and ellipticity are a function of pump power.
It would be highly desirable to produce an output beam from a laser using an anisotropic material that is substantially round and is a diffraction limited gaussian beam. This type of output beam would be particularly attractive for Nd:YVO4 crystals.